there’s a school of thought which says that deficits are never a problem, as long as a country can issue its own currency. The most prominent advocate of this view is probably Jamie Galbraith, but he’s not alone.

Krugman is undoubtedly referring to Modern Monetary Theory (MMT)/neo-Chartalism. However, he is wrong to accuse neo-Chartalists of thinking that “deficits are never a problem.” In fact, Modern Monetary Theory says that, even though deficits are not “financially” constrained, they face real constraints in available resources, capacity utilization, the unemployment level, the exchange rate, the external balance, and inflation rate.

This is quite different from saying that “deficits are never a problem.” Clearly deficits can be, if they cause excessive inflation and push the current account deficit to an unsustainable level. Investor confidence is also a factor influencing the exchange rate, but, since behaviour in these financial markets is fundamentally irrational and subject to panics, one cannot predict what they will do, and the government should not be held hostage by them.

Krugman has misunderstood Galbraith. If we look at what Galbraith actually says, it is very clear:

[sc there is a] common belief that the government must borrow in order to spend, and thus that the government faces “funding risks” in private markets. Such risks exist … for private individuals, for companies, for state and local governments, and for national governments such as Greece that have ceded monetary sovereignty to a central bank. But the situation of the United States government is quite different. The U.S. government spends (and the Federal Reserve lends) in a very simple way. It does so by writing checks – in fact simply by marking up numbers in a computer. Those numbers then appear in the bank accounts of the payees, who may be government employees, private contractors, or the recipients of federal transfer programs. The effect of government check-writing is to create a deposit in the banking system. This is a “free reserve.” Banks of course prefer to earn interest on their reserves. Thus they demand a US Treasury bond, which pays more interest without incurring any form of credit or default risk … The Treasury can meet that demand, or not, at its option – it can permit, or not permit, the stock of US Treasury bonds in circulation to increase. So long as U.S. banks are required to accept U.S. government checks – which is to say so long as the Republic exists – then the government can and does spend without borrowing, if it chooses to do so. And, if it chooses to issue Treasuries to meet the demand, it can do that as well. There is never a shortfall of demand for Treasury bonds; Treasury auctions do not fail …. Insolvency, bankruptcy, or even higher real interest rates are not among the actual risks to this system. The actual risks in this system are (to a minor degree) inflation, and to a larger degree, depreciation of the dollar.

Galbraith is entirely right, and Krugman omits the words in bold, and from these words it is quite clear that Galbraith understands that there are real constraints on deficit spending, not phantom “financial” ones. Moreover, it is perfectly clear that Galbraith is talking about deficit spending during a period of high unemployment and low capacity utilization, and perhaps even in the face of a double dip recession.

In his response to Galbraith, Krugman adopts the flawed quantity theory of money and attempts to prove mathematically what is perfectly obvious: that hyperinflation can result from continuous budget deficits that are monetized by the central bank. But, since Modern Monetary Theory already acknowledges that inflation is a real constraint on deficit spending, Krugman’s analysis seems rather pointless.

So when the government pays a check, it will create a bank account and add to the supply of money, for outside the system (which you call the vertical component of money).

But when the government makes an open-market operation, it creates more government debt. Should this still be considered "the vertical component of money" or is it "the horizontal component of money", as it requires balancing of liabilities against assets?

I also don't know if the act of paying a check by the government should be considered "deficit spending".

Of course, that spending must have some limits, such as the risk of high inflation....

That is what I said above. The contraints to deficit spending or any type of govenrment spending are real (= available resources, capacity utilization, the unemployment level, the exchange rate, the external balance, and inflation rate.), not financial.

"So when the government pays a check, it will create a bank account and add to the supply of money...."

It breaks with lots of myths and disbeliefs (mostly held by free market economists) and it's a great framework about how most governments finance themselves.

I think it still doesn't address my question:

"But when the government makes an open-market operation, it creates more government debt. Should this still be considered "the vertical component of money" or is it "the horizontal component of money", as it requires balancing of liabilities against assets?"

I think that most policy considerations stated in the article are not derived from MMT but instead are inherited from a Keynesian view (it assumes the aggregate demand problem).

The fact that the non-government sector can only be provided net financial assets (net savings) by government making cumulative deficit spending only holds for nominal values (cash balances and other financial assets) which will obviously impact real values. But more "real savings" will be made without this spending, because the purchasing power of money will rise (price deflation).

So well, I guess you will acknowledge that and say that price deflation, even if slow and constant, will be the cause of a shortage of aggregate demand and further involuntary unemployment (and probably less resources and capacity utilization).

I would really appreciate if you could point me out something to read about it (this is the root of the Keynesian policies, I think). Also, you seem to acknowledge that price deflation is one of the consequences of the instability of financial markets (maybe I'm wrong). Do you consider this as the main factor of the problem of aggregate demand?